I had a co-worker, in a different office than me, who had two of the same shirt. She decided to wear only those two shirts to work until somebody said something. A little more than 3 weeks later and someone finally commented on it.

Your primary Switch shouldn’t need to do that, and it also would have done it if you didn’t get the DLC. It is dumb that it basically requires internet access for all your additional Switches to operate, and it actually promotes you marking your travel switch as the primary device while the actual primary device sits at home where you always have internet access.